The Poling Process in Detail 555 12.6.3 Models The excellent agreement between experiments and a two-ion model [88,120] obtained when a low-mobility species (e.g., H 3 O þ ) replaces a highly mobile one (e.g., Na þ ) is illustrated by the example given in Fig. 12.11 (from reference [120]). The measured profile of the induced w (2) in samples poled for different time intervals (Fig. 12.11a) is compared with the theoretical predictions of the nonlinear profile expected according to the model (Fig. 12.11b). The technique for the experimental determination of w (2) was that of measuring SHG while etching with the arrangement shown in Fig. 12.7 and the application of "layer peeling" [97]. Figure 12.12a shows the theoretical and experimental values of the peak w (2) , and part (b) shows the width of the depletion region for various poling times, both determined with the same techniques as in Fig. 12.11. The ion-exchange model is based on solving Poisson's equation and the equa- tion of continuity for the electric field E and the carrier concentration, which in one dimension can be written as [120] @p Na @ðp Na EÞ @ 2 p Na ¼ Àm Na þ D Na @t @x 2 @x @p H @ðp H EÞ @ 2 p H